scholarly journals The computation of zeros of Ahlfors map for multiply connected regions

2017 ◽  
Author(s):  
Kashif Nazar ◽  
Ali H. M. Murid ◽  
Ali W. K. Sangawi
Keyword(s):  
Multiply Connected ◽  
Ahlfors Map ◽  
Multiply Connected Regions

Integral Equation for the Ahlfors Map on Multiply Connected Regions

2015 ◽  
Vol 73 (1) ◽  
Author(s):  
Kashif Nazar ◽  
Ali H. M. Murid ◽  
Ali W. K. Sangawi
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Connected Region ◽  
Multiply Connected ◽  
Multiple Method ◽  
Boundary Correspondence ◽  
Ahlfors Map ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

This paper presents a new boundary integral equation with the adjoint Neumann kernel associated with  where  is the boundary correspondence function of Ahlfors map of a bounded multiply connected region onto a unit disk. The proposed boundary integral equation is constructed from a boundary relationship satisfied by the Ahlfors map of a multiply connected region. The integral equation is solved numerically for  using combination of Nystrom method, GMRES method, and fast multiple method. From the computed values of    we solve for the boundary correspondence function  which then gives the Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method.

scholarly journals A characterization of internal functions on multiply connected regions

1984 ◽  
Vol 96 ◽  
pp. 23-28
Author(s):  
Lee A. Rubel
Keyword(s):  
Hardy Spaces ◽  
Multiply Connected ◽  
Multiply Connected Regions ◽  
Internal Function

The notion of internal function enters naturally in the study of factorization of function in Lumer’s Hardy spaces—see [RUB], where this aspect is developed in some detail.

scholarly journals Circular Slits Map of Bounded Multiply Connected Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ali W. K. Sangawi ◽  
Ali H. M. Murid ◽  
M. M. S. Nasser
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Connected Region ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

We present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a circular slit region. The method is based on some uniquely solvable boundary integral equations with adjoint classical, adjoint generalized, and modified Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method.

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